NCERT Exemplar Class 7 Maths Chapter 8 Rational Numbers

In this chapter, we provide NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 8 Rational Numbers for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 8 Rational Numbers pdf. Now you will get step by step solution to each question.

NCERT Exemplar Class 7 Maths Chapter 8 Rational Numbers

Multiple Choice Questions (MCQs)

Question 1:
A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and
(a) q = 0                               (b) q = 1
(c) q ≠ 1                                 (d) q ≠ 0
Solution :
(d) By definition, a number that can be expressed in the form of p/q, where p and q are integers and q≠0, is called a rational number.

Question 2:
Which of the following rational numbers is positive?


Solution :
(c) We know that, when numerator and denominator of a rational number, both are negative,
it is a positive rational number.
Hence, among the given rational numbers is positive.

Question 3:
Which of the following rational numbers is negative?

Solution :

Question 4:
In the standard form of a rational number, the common factor of numerator and denominator is always
(a) 0        (b) 1        c) -2        (d)2
Solution :
(b) By definition, in the standard form of a rational number, the common factor of numerator and denominator is always1
Note: Common factor means, a number which divides both the given two numbers.

Question 5:
Which of the following rational numbers is equal to its reciprocal?
(a) 1        (b) 2        c) 1/2        (d)0
Solution :

Question 6:
The reciprocal of 1/2 is
(a) 3        (b) 2        c) -1       (d)0
Solution :
(b) Reciprocal of =2

Question 7:
The standard form of is

Solution :

Question 8:
Which of the following is equivalent to 4/5 ?

Solution :

Note: If the numerator and denominator of a rational number is multiplied/divided by a non-zero integer, then the result we get, is equivalent rational number.

Question 9:
How many rational numbers are there between two rational numbers?
(a) 1                                                               (b) 0
(c) unlimited                                               (d) 100
Solution :
(c) There are unlimited numbers between two rational numbers.

Question 10:
In the standard form of a rational number, the denominator is always a
(a) 0                                                               (b) negative  integer
(c) positive integer                                      (d) 1
Solution :
(c) By definition, a rational number is said to be in the standard form, if its denominator is a positive integer.

Question 11:
To reduce a rational number to its standard form, we divide its numerator and denominator by their
(a) LCM                                                       (b)    HCF
(c) product                                                  (d)    multiple
Solution :
(b) To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF.

Question 12:
Which is greater number in the following?
(a) –                           (b) 0                             (c)                       (d)-2
Solution :

Fill in the Blanks

In questions 13 to 46, fill in the blanks to make the statements true.

Question 13:
 is a rational number
Solution :
The given rational number is a negative number, because its numerator is negative integer.
Hence, is a negative rational number.

Question 14:
is a____rational number.
Solution :
The given rational number 1 is positive number, because its numerator and denominator are positive integer.
Hence, 1 is a positive rational number.

Question 15:
The standard form of is______ .
Solution :

Question 16:
The standard form of is______ .
Solution :

Question 17:
On a number line, is to the______of Zero(0).
Solution :

Note All the negative numbers lie on the left side of zero on the number line

Question 18:
On a number line, is to the______of Zero(0).
Solution :
On a number line, is to the right of Zero(0).

Note All the positive numbers lie on the right side of zero on the number line.

Question 19:
is _____ than .
Solution :

Question 20:
 is _____ than 0.
Solution :

Question 21:
and represent_______ rational numbers.
Solution :

Question 22:
and represent_______ rational numbers.
Solution :

Question 23:
Additive inverse of  is_____.
Solution :
Since, additive inverse is the negative of a number.
Hence, additive inverse of is .
Note Additive inverse is a number, which when added to a given number, we get result as zero.

Question 24:
+ = _____.
Solution :

Question 25:
+  = ______.
Solution :

Question 26:
= _____.
Solution :

Question 27:
= _____.
Solution :

Question 28:
Given, 
Solution :

Question 29:
=
Solution :

Question 30:
–  = _____
Solution :

In questions 31  to 35,  fill in the boxes with the correct symbol ‘<‘,'<‘ or ‘=’.

Question 31:

Solution :

Question 32:

Solution :

Question 33:

Solution :

Question 34:

Solution :

Question 35:

Solution :

Question 36:
The reciprocal of_______ does not exist.
Solution :
The reciprocal of zero does not exist, as reciprocal of 0 is 1/0, which is not defined.

Question 37:
The reciprocal of 1 is_______
Solution :
The reciprocal of 1=1/1
Hence, the reciprocal of 1 is 1.

Question 38:
=________
Solution :

Question 39:
=_________
Solution :

Question 40:
=_________
Solution :
Hence, =0
Because, zero multiplies by any number result is zero.

Question 41:
_____ x  =1
Solution :

Question 42:
The standard form of rational number – 1 is_______.
Solution :
∴ HCF of given rational number -1 is 1.
For standard form = -1 +1 = -1
Hence, the standard form of rational number -1 is -1.

Question 43:
 If m is a common divisor of a and b, then 
Solution :

Question 44:
If p and q are positive integers, then is a______ rational number and is a_____ rational number.
Solution :
if p and q are positive integers, then p/q is a positive rational number, because both numerator and denominator are positive and is a negative rational number, because denominator is in negative

Question 45:
Two rational numbers are said to be equivalent or equal, if they have the same_______form.
Solution :
Two rational numbers are said to be equivalent or equal, if they have the same simplest form.

Question 46:
If p/q is a rational number, then q cannot be_____________
Solution :
By definition, if B is a rational number, then q cannot be zero.

True/False

In questions 47 to 65, state whether the following statements are True or False.

Question 47:
Every natural number is a rational number, but every rational number need not be a natural number.
Solution :
True
e.g. 1/2 is a rational number, but not a natural number.

Question 48:
Zero is a rational number.
Solution :
True
e.g. Zero can be written as 0 = 0/1. We know that, a number of the form , where p, q are integers and q ≠ 0 is a rational number. So, zero is a rational number.

Question 49:
Every integer is a rational number but every rational number need not be an integer.
Solution :
True
Integers…. – 3,-2,-1, 0,1,2, 3,…
Rational numbers:
……
Hence, every integer is rational number, but every rational number is not an integer.

Question 50:
Every negative integer is not a negative rational number.
Solution :
False
Because all the integers are rational numbers, whether it is negative/positive but vice-versa is not true.

Question 51:
If is a rational number and m is a non-zero integer, then

Solution :
True
e.g. Let m = 1,2, 3,…

Note: When both numerator and denominator of a rational number are multiplied/divide by a same non-zero number, then we get the same rational number

Question 52:
If is a rational number and m is a non-zero common divisor of p and q, then

Solution :

Question 53:
In a rational number, denominator always has to be a non-zero integer.
Solution :
Basic definition of the rational number is that, it is in the form of , where q ≠ 0. It is because any number divided by zero is not defined.

Question 54:
If  is a rational number and m is a non-zero integer, then   is a rational number not equivalent to .
Solution :

Question 55:
Sum of two rational numbers is always a rational number.
Solution :
True
Sum of two rational numbers is always a rational number, it is true.

Question 56:
All decimal numbers are also rational numbers.
Solution
True
All decimal numbers are also rational numbers, it is true.

Question 57:
The quotient of two rationals is always a rational number.
Solution :
False
The quotient of two rationals is not always a rational number.
e.g. 1/0.

Question 58:
Every fraction is a rational number.
Solution :
True
Every fraction is a rational number but vice-versa is not true.

Question 59:
Two rationals with different numerators can never be equal.
Solution :
False

Question 60:
8 can be written as a rational number with any integer as denominator.
Solution :
8 can be written as a rational number with any integer as denominator, it is false because 8 can be written as a rational number with 1 as denominator i.e.8/1.

Question 61:
is equivalent to 
Solution :
True

Question 62:
The rational number lies to the right of zero on the number line.
Solution :
False

Question 63:
The rational number and are on the opposite sides of zero on the number line.
Solution :

Question 64:
Every rational number is a whole number.
Solution :
False
e.g. is a rational number, but it is not a whole number, because whole numbers are  0,1,2….

Question 65:
Zero is the smallest rational number.
Solution :
False
Rational numbers can be negative and negative rational numbers are smaller than zero.

Question 66:
Match the following:

Solution :

Question 67:
Write each of the following rational numbers with positive denominators.

Solution :

Question 68:
Express as a rational number with denominator:
(a)36     (b) — 80
Solution :

Question 69:
Reduce each of the following rational numbers in its lowest form
(i) 
(ii) 
Solution :

Question 70:
Express each of the following rational numbers in its standard form

Solution :

Question 71:
Are the rational numbers and equivalent? Give reason.
Solution :

Question 72:
Arrange the rational numbers  in ascending order.
Solution :

Question 73:
Represent the following rational numbers on a number line.

Solution :

Question 74:
If = find the value of x.
Solution :

Question 75:
Give three rational numbers equivalent to
(i)
(ii)
Solution :

Question 76:
Write the next three rational numbers to complete the pattern:

Solution :

Question 77:
List four rational numbers between  and .
Solution :

Question 78:
Find the sum of

Solution :

Question 79:
Solve:

Solution :

Question 80:
Find the product of

Solution :

Question 81:
Simplify:

Solution :

Question 82:
Simplify:

Solution :

Question 83:
Which is greater in the following?

Solution :

Question 84:
Write a rational number in which the numerator is less than ‘-7 x 11′ and the denominator is greater than ’12+ 4’.
Solution :

Question 85:
If x =   and y = , then evaluate x + y, x-y, xxy and x ÷ y.
Solution :

Question 86:
Find the reciprocal of the following:

Solution :

Question 87:
Complete the following table by finding the sums.

Solution :

Question 88:
Write each of the following numbers in the form p/q, where p and q are  integers.
(a) six-eighths            (b) three and half
(c) opposite of 1         (d) one-fourth
(e) zero                        (f) opposite of three-fifths
Solution :

Question 89:
 =
Solution :

Question 90:
Given that, and are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers, we say that

Solution :

Question 91:
In each of the following cases, write the rational number whose numerator and denominator are respectively as under:
(a) 5-39 and 54-6                         (b) (- 4) x 6 and 8 ÷ 2
(c) 35 ÷ (- 7) and 35 -18               (d) 25 +15 and 81÷40
Solution :

Question 92:
Write the following as rational numbers in their standard forms.

Solution :

Question 93:
Find a rational number exactly halfway between

Solution :

Question 94:

Solution :

Question 95:
What should be added to to obtain the nearest natural number?
Solution :

Question 96:
What should be subtracted from to obtain the nearest integer?
Solution :

Question 97:
What should be multiplied with to obtain the nearest integer?
Solution :

Question 98:
What should be divided by to obtain the greatest negative integer?
Solution :

Question 99:
From a rope 68 m long, pieces of equal size are cut. If length of one piece is m, find the number of such pieces.
Solution :

Question 100:
If 12 shirts of equal size can be prepared from 27 m cloth, what is length of cloth required for each shirt?
Solution :

Question 101:
Insert 3 equivalent rational numbers between

Solution :

Question 102:
Put the (✓), wherever applicable

Solution :

Question 103:
‘o’ and ‘b’ are two different numbers taken from the numbers 1-50. What is the largest value that can have? What is the largest can have?
Solution :

Question 104:
150 students are studying English, Maths or both. 62% of the students are studying English and 68% are studying Maths. How many students are studying both?
Solution :

Question 105:
A body floats of its volume above the surface. What is the ratio of the body submerged volume to its exposed volume? Rewrite it as a rational number.
Solution :

In questions 106 to 109, find the odd one out of the following and give reason.

Question 106:

Solution :

Question 107:

Solution :

Question 108:

Solution :

Question 109:

Solution :
From the above given rational numbers, we can see that is in its lowest form while others have common factor in numerator and denominator.

Question 110:
What’s the Error? Chhaya simplified a rational number is this manner   =  What error did the student make?
Solution :

All Chapter NCERT Exemplar Problems Solutions For Class 7 maths

—————————————————————————–

All Subject NCERT Exemplar Problems Solutions For Class 7

*************************************************

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share ncertexemplar.com to your friends.